Background

This document has nls (non-linear least squares) regression fits using the LOG-NORMAL functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Log-Normal functional form \(B = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot biomass interval, which is defined as the measurement time minus 10 years and a 30-year climate normal from 1960-1989, and \(yr\) is the measurement year (all FIA data). Free parameters are \(ge\): biomass growth enhancement over time, \(\alpha\): the growth compensation of lost plot biomass, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(B\), \(c\): the \(StdAge\) value at peak \(B\), and \(d\): the log-normal curve shape parameter.

Model selection is used to determine the best fitting models including \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period) and \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).

model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 3: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)

Note:

This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval

This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Error in eval(extras, data, env) : object 'P_211' not found
## Error in eval(extras, data, env) : object 'P_211' not found
##   model      AIC
## 1     1       NA
## 2     2       NA
## 3     3 72677.43
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    5.614e-01  2.059e-01   2.726  0.00642 ** 
## phi   9.854e-03  6.256e-03   1.575  0.11528    
## alpha 8.465e-01  2.725e-02  31.064  < 2e-16 ***
## a     4.030e+01  1.937e+00  20.805  < 2e-16 ***
## b     1.073e+02  5.001e+00  21.459  < 2e-16 ***
## c     1.144e+02  4.148e+00  27.588  < 2e-16 ***
## d     9.190e-01  3.966e-02  23.173  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4627 on 6798 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq   F value Pr(>F)    
## 1  18747     6234.1                               
## 2  18742     6234.1  5   0.04    0.0268 0.9997    
## 3  18741     5853.7  1 380.34 1217.6643 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 195208.2
## 2     2 195169.6
## 3     3 193991.4
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.673e-01  1.141e-01   4.096 4.23e-05 ***
## phi   0.000e+00  3.595e-03   0.000        1    
## alpha 7.596e-01  1.808e-02  42.006  < 2e-16 ***
## a     2.390e+01  7.237e-01  33.023  < 2e-16 ***
## b     8.004e+01  2.147e+00  37.277  < 2e-16 ***
## c     1.108e+02  3.013e+00  36.762  < 2e-16 ***
## d     1.189e+00  2.983e-02  39.855  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5589 on 18741 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   7164     1238.0                             
## 2   7163     1238.0  1   0.00   0.000      1    
## 3   7154     1100.4  9 137.59  99.388 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 78202.93
## 2     2 78204.93
## 3     3 77298.20
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.118e-01  1.271e-01   1.666   0.0957 .  
## phi   0.000e+00  4.599e-03   0.000   1.0000    
## alpha 8.317e-01  2.587e-02  32.154   <2e-16 ***
## a     3.054e+01  2.330e+00  13.106   <2e-16 ***
## b     1.625e+02  7.450e+00  21.811   <2e-16 ***
## c     1.347e+02  9.012e+00  14.946   <2e-16 ***
## d     1.333e+00  6.538e-02  20.387   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3922 on 7154 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (9 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   4868     1470.5                              
## 2   4867     1469.8  1   0.698  2.3127 0.1284    
## 3   4860     1351.4  7 118.452 60.8552 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 52441.03
## 2     2 52440.72
## 3     3 51990.44
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.046083   0.204593  -0.225   0.8218    
## phi     0.022445   0.009502   2.362   0.0182 *  
## alpha   0.888690   0.039183  22.681   <2e-16 ***
## a      26.487141   1.915801  13.826   <2e-16 ***
## b     120.168676   5.959752  20.163   <2e-16 ***
## c     107.013685   5.097928  20.992   <2e-16 ***
## d       1.053641   0.051099  20.620   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5273 on 4860 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (10 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9567, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -31.414, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   8771     1614.1                             
## 2   8770     1614.1  1   0.00    0.00 0.9999    
## 3   8766     1487.3  4 126.79  186.82 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 92044.88
## 2     2 92046.88
## 3     3 91308.18
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    7.240e-02  1.103e-01   0.656    0.512    
## phi   0.000e+00  5.223e-03   0.000    1.000    
## alpha 7.809e-01  2.666e-02  29.292   <2e-16 ***
## a     3.121e+01  2.276e+00  13.712   <2e-16 ***
## b     1.074e+02  3.942e+00  27.247   <2e-16 ***
## c     1.078e+02  4.925e+00  21.882   <2e-16 ***
## d     1.264e+00  5.982e-02  21.138   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4119 on 8766 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (10 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1  12326     3355.8                             
## 2  12325     3355.8  1   0.00     0.0      1    
## 3  12324     2995.8  1 360.03  1481.1 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 133924.2
## 2     2 133926.2
## 3     3 132528.8
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.758e+00  1.507e-01   11.67   <2e-16 ***
## phi   0.000e+00  4.345e-03    0.00        1    
## alpha 7.243e-01  1.419e-02   51.04   <2e-16 ***
## a     2.473e+01  7.808e-01   31.68   <2e-16 ***
## b     1.068e+02  3.870e+00   27.59   <2e-16 ***
## c     1.080e+02  6.116e+00   17.66   <2e-16 ***
## d     1.475e+00  4.881e-02   30.23   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.493 on 12324 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (16 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq   F value    Pr(>F)    
## 1  12425     5068.8                                  
## 2  12424     5065.8  1   3.00    7.3664  0.006655 ** 
## 3  12423     4612.3  1 453.42 1221.2549 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 137933.1
## 2     2 137927.8
## 3     3 136764.2
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.068e+00  1.492e-01   7.157 8.69e-13 ***
## phi   1.441e-02  5.553e-03   2.595  0.00948 ** 
## alpha 7.468e-01  1.525e-02  48.953  < 2e-16 ***
## a     2.835e+01  1.066e+00  26.591  < 2e-16 ***
## b     1.178e+02  5.361e+00  21.968  < 2e-16 ***
## c     1.222e+02  9.516e+00  12.842  < 2e-16 ***
## d     1.516e+00  6.354e-02  23.863  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6093 on 12423 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (40 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Error in nls(f_ln_3, data = G_234, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1258     341.03                          
## 2   1257     340.57  1 0.45741  1.6882 0.1941
##   model      AIC
## 1     1 14066.84
## 2     2 14067.14
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)
## ge 3.821e-02  3.664e-01   0.104    0.917
## a  1.252e+01  1.911e+01   0.655    0.512
## b  8.328e+02  2.810e+03   0.296    0.767
## c  5.000e+03  3.947e+04   0.127    0.899
## d  3.188e+00  3.021e+00   1.055    0.292
## 
## Residual standard error: 0.5207 on 1258 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96304, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.433, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in nls(f_ln_1, data = G_242, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_3, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_242.", Mod.Sel1, sep = "")) : 
##   object 'nls_242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   1791     389.13                              
## 2   1790     389.12  1  0.015   0.0689  0.793    
## 3   1789     367.65  1 21.464 104.4440 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18723.44
## 2     2 18725.38
## 3     3 18625.47
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.19924    0.32180   0.619    0.536    
## phi     0.00000    0.01253   0.000    1.000    
## alpha   0.74888    0.06801  11.011  < 2e-16 ***
## a      25.68778    4.97871   5.160 2.75e-07 ***
## b     100.74277    8.91977  11.294  < 2e-16 ***
## c     104.42177    8.31177  12.563  < 2e-16 ***
## d       1.14789    0.10986  10.449  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4533 on 1789 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96836, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.468, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    656     205.66                                
## 2    655     205.66  1  0.000   0.000         1    
## 3    654     185.92  1 19.741  69.442 4.632e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6693.871
## 2     2 6695.871
## 3     3 6631.168
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.15981    0.38048  -0.420    0.675    
## phi    0.00000    0.02663   0.000    1.000    
## alpha  0.77294    0.08344   9.263  < 2e-16 ***
## a     20.69404    4.82816   4.286 2.09e-05 ***
## b     79.86186    9.27057   8.615  < 2e-16 ***
## c     63.52929    7.13466   8.904  < 2e-16 ***
## d      1.14819    0.15584   7.368 5.25e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5332 on 654 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94196, p-value = 2.149e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.367, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

## Error in nls(f_ln_1, data = G_261, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_261, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_3, data = G_261, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_261.", Mod.Sel1, sep = "")) : 
##   object 'nls_261.' not found

summary

  • simple model: does not fit

  • phi model: does not fit

  • phi-alpha model: does not fit

  • unable to fit model (only 64 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_262.", Mod.Sel1, sep = "")) : 
##   object 'nls_262.' not found

summary

  • simple model: does not fit

  • phi model: does not fit

  • phi-alpha model: does not fit

  • unable to fit model (0 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Error in nls(f_ln_3, data = G_263, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: false convergence (8)
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    149     26.638                              
## 2    148     26.638  1 -3.6088e-11       0      1
##   model      AIC
## 1     1 1935.134
## 2     2 1937.134
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge    1.224      2.254   0.543   0.5879  
## a     0.000     69.109   0.000   1.0000  
## b  1000.000    913.184   1.095   0.2753  
## c  1898.226   4726.971   0.402   0.6886  
## d     2.777      1.518   1.830   0.0693 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4228 on 149 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97748, p-value = 0.0126
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.2016, p-value = 0.0277
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Error in nls(f_ln_1, data = G_313, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_313, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_3, data = G_313, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_313.", Mod.Sel1, sep = "")) : 
##   object 'nls_313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    298     169.14                         
## 2    297     169.14  1 0.0000  0.0000 1.0000
## 3    296     167.90  1 1.2399  2.1858 0.1404
##   model      AIC
## 1     1 3100.582
## 2     2 3102.582
## 3     3 3102.353
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.4889     1.4827   0.330   0.7418  
## a    0.0000    19.2900   0.000   1.0000  
## b   52.4290    27.5134   1.906   0.0577 .
## c  119.8342    66.7961   1.794   0.0738 .
## d    2.1713     1.2242   1.774   0.0771 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7534 on 298 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.8809, p-value = 1.318e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.2814, p-value = 3.356e-10
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Error in nls(f_ln_1, data = G_332, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_332, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_3, data = G_332, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_332$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_332.", Mod.Sel1, sep = "")) : 
##   object 'nls_332.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(f_ln_1, data = G_342, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_3, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_342.", Mod.Sel1, sep = "")) : 
##   object 'nls_342.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6721     1270.3                                 
## 2   6720     1264.3  1   6.032   32.06 1.557e-08 ***
## 3   6719     1085.2  1 179.120 1109.04 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 71115.80
## 2     2 71085.79
## 3     3 70060.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.245e-01  1.530e-01   2.775  0.00554 ** 
## phi   2.541e-02  5.584e-03   4.550 5.45e-06 ***
## alpha 8.215e-01  2.232e-02  36.804  < 2e-16 ***
## a     1.751e+01  2.891e+00   6.057 1.47e-09 ***
## b     1.531e+02  1.030e+01  14.864  < 2e-16 ***
## c     1.961e+02  2.327e+01   8.430  < 2e-16 ***
## d     1.631e+00  1.078e-01  15.122  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4019 on 6719 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   8027     1280.2                             
## 2   8026     1280.2  1  0.000    0.00      1    
## 3   8025     1188.2  1 92.026  621.53 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 88546.92
## 2     2 88548.92
## 3     3 87951.76
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    9.518e-01  1.253e-01   7.595 3.44e-14 ***
## phi   0.000e+00  4.205e-03   0.000        1    
## alpha 8.478e-01  3.179e-02  26.673  < 2e-16 ***
## a     3.887e+01  2.121e+00  18.330  < 2e-16 ***
## b     1.129e+02  3.539e+00  31.916  < 2e-16 ***
## c     9.991e+01  2.742e+00  36.436  < 2e-16 ***
## d     1.168e+00  4.351e-02  26.839  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3848 on 8025 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Error in nls(f_ln_1, data = G_M223, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_M223, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     1       NA
## 2     2       NA
## 3     3 8818.569
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -6.054e-01  2.277e-01  -2.659  0.00798 ** 
## phi    7.662e-02  1.800e-02   4.257  2.3e-05 ***
## alpha  8.905e-01  7.124e-02  12.500  < 2e-16 ***
## a      0.000e+00  4.759e+01   0.000  1.00000    
## b      3.440e+02  6.861e+02   0.501  0.61621    
## c      1.654e+03  1.060e+04   0.156  0.87595    
## d      3.294e+00  3.719e+00   0.886  0.37607    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3373 on 875 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96709, p-value = 3.239e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.555, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Error in nls(f_ln_1, data = G_M231, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_M231, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     1       NA
## 2     2       NA
## 3     3 10131.35
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    5.135e-01  5.352e-01   0.959   0.3376    
## phi   7.733e-03  2.242e-02   0.345   0.7302    
## alpha 7.642e-01  7.743e-02   9.870   <2e-16 ***
## a     1.667e+01  8.120e+00   2.053   0.0404 *  
## b     1.758e+02  1.157e+02   1.519   0.1290    
## c     4.206e+02  6.048e+02   0.695   0.4869    
## d     2.147e+00  8.579e-01   2.502   0.0125 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.453 on 980 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96207, p-value = 2.47e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.989, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   3172     1918.7                             
## 2   3171     1918.7  1   0.00  0.0000      1    
## 3   3148     1790.5 23 128.11  9.7928 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 41988.35
## 2     2 41990.35
## 3     3 41548.04
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.18061    0.49156  -0.367 0.713331    
## phi     0.00000    0.01505   0.000 1.000000    
## alpha   1.10192    0.06873  16.033  < 2e-16 ***
## a       3.55424   13.98067   0.254 0.799338    
## b     568.48059   92.86868   6.121 1.04e-09 ***
## c     667.30946  174.01443   3.835 0.000128 ***
## d       2.21626    0.22808   9.717  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7542 on 3148 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (24 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95105, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -17.577, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value    Pr(>F)    
## 1   1952    1001.42                                 
## 2   1951     925.67  1 75.745 159.6441 < 2.2e-16 ***
## 3   1935     894.94 16 30.737   4.1537 5.856e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24765.07
## 2     2 24613.15
## 3     3 24401.78

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91612, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.034, p-value = 0.002414
## alternative hypothesis: two.sided

predict and plot

## Warning in mean.default(G_M261$MEASTIM, na.rm = TE): argument is not numeric or
## logical: returning NA
## Warning: Removed 1000 row(s) containing missing values (geom_path).

plotting 2

## Warning: Removed 20 rows containing missing values (geom_point).
## Warning: Removed 20 rows containing missing values (geom_pointrange).

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1    356     110.33                               
## 2    355     109.15  1 1.1717  3.8108 0.051710 .  
## 3    354     105.62  1 3.5361 11.8518 0.000645 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3771.802
## 2     2 3769.947
## 3     3 3760.059
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.81573    0.33677  -5.392 1.28e-07 ***
## phi     0.04237    0.02511   1.688 0.092361 .  
## alpha   0.50499    0.13502   3.740 0.000214 ***
## a      54.76880   15.65852   3.498 0.000529 ***
## b     184.32447   40.04085   4.603 5.80e-06 ***
## c     158.85154   25.00796   6.352 6.53e-10 ***
## d       0.81683    0.15947   5.122 4.97e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5462 on 354 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94156, p-value = 9.985e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.18153, p-value = 0.856
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   1691     583.39                              
## 2   1690     583.09  1  0.308   0.8923  0.345    
## 3   1689     527.98  1 55.108 176.2917 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 17699.64
## 2     2 17700.75
## 3     3 17534.37
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.07060    0.29359  -3.647 0.000274 ***
## phi     0.01782    0.01162   1.534 0.125224    
## alpha   0.64315    0.04157  15.472  < 2e-16 ***
## a      41.57156    5.51472   7.538 7.73e-14 ***
## b     135.46943   16.29218   8.315  < 2e-16 ***
## c     212.14212   23.03599   9.209  < 2e-16 ***
## d       1.23436    0.11259  10.963  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5591 on 1689 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92964, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.9597, p-value = 7.058e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   2641     1154.9                              
## 2   2640     1151.5  1  3.413  7.8251 0.00519 ** 
## 3   2617     1078.3 23 73.212  7.7253 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28864.48
## 2     2 28858.65
## 3     3 28506.38
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.73312    0.75925   0.966  0.33434    
## phi     0.03805    0.01345   2.828  0.00472 ** 
## alpha   0.63197    0.04647  13.598  < 2e-16 ***
## a      25.71790    4.64424   5.538 3.37e-08 ***
## b      99.70475   17.65984   5.646 1.82e-08 ***
## c     210.36985   18.10340  11.620  < 2e-16 ***
## d       1.24064    0.09401  13.197  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6419 on 2617 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (25 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89938, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6907, p-value = 2.722e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   1665     654.15                              
## 2   1664     653.64  1  0.511   1.3008 0.2542    
## 3   1663     607.37  1 46.266 126.6784 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18742.43
## 2     2 18743.13
## 3     3 18622.53
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      2.49946    1.96354   1.273  0.20322    
## phi     0.01486    0.01732   0.858  0.39089    
## alpha   0.70768    0.05537  12.781  < 2e-16 ***
## a      17.72088    5.65869   3.132  0.00177 ** 
## b      88.45316   27.94636   3.165  0.00158 ** 
## c     132.83193    5.59014  23.762  < 2e-16 ***
## d       0.97930    0.04976  19.680  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6043 on 1663 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (5 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93649, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.1382, p-value = 3.5e-05
## alternative hypothesis: two.sided

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    356     147.67                                 
## 2    355     146.35  1  1.3214  3.2053   0.07425 .  
## 3    354     127.38  1 18.9706 52.7223 2.459e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3622.910
## 2     2 3621.665
## 3     3 3573.547
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -1.030e+00  4.880e-01  -2.111   0.0355 *  
## phi    5.401e-03  3.136e-02   0.172   0.8633    
## alpha  7.993e-01  9.457e-02   8.452 7.54e-16 ***
## a      0.000e+00  7.695e+01   0.000   1.0000    
## b      1.379e+02  2.192e+02   0.629   0.5295    
## c      7.728e+02  4.021e+03   0.192   0.8477    
## d      3.138e+00  4.935e+00   0.636   0.5253    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5999 on 354 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94196, p-value = 1.11e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.6772, p-value = 2.436e-11
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    207     64.472                                
## 2    206     64.472  1 0.0000   0.000 0.9999985    
## 3    205     60.643  1 3.8286  12.942 0.0004027 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2088.502
## 2     2 2090.502
## 3     3 2079.523
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.88598    0.37590  -5.017 1.13e-06 ***
## phi     0.00000    0.05799   0.000 1.000000    
## alpha   0.50427    0.12433   4.056 7.10e-05 ***
## a      36.45861    9.41288   3.873 0.000144 ***
## b     126.50101   26.04280   4.857 2.36e-06 ***
## c     150.15616   16.92871   8.870 3.62e-16 ***
## d       0.93149    0.16914   5.507 1.08e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5439 on 205 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93284, p-value = 2.735e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.89551, p-value = 0.3705
## alternative hypothesis: two.sided

predict and plot

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3
212 Laurentian Mixed Forest 3
221 Eastern Broadleaf Forest 3
222 Midwest Broadleaf Forest 3
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3
232 Outer Coastal Plain Mixed Forest 3
234 Lower Mississippi Riverine Forest 1
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3
255 Prairie Parkland (Subtropical) 3
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest 1
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe 1
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest 3
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 3
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 3
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow 3

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.2.5 ge.97.5 phi phi.2.5 phi.97.5 alpha alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6806 2847 0.5614145 0.1577549 0.9650741 0.0098539 -0.0024099 0.0221177 0.8464830 0.7930648 0.8999011 40.304388 36.5067722 44.10200 107.31646 97.512853 117.12006 114.42661 106.29574 122.55748 0.9189999 0.8412571 0.9967427
212 Laurentian Mixed Forest east 18775 8891 0.4673302 0.2436774 0.6909831 0.0000000 -0.0070458 0.0070458 0.7596243 0.7241785 0.7950701 23.899941 22.4813449 25.31854 80.03947 75.830899 84.24804 110.76006 104.85445 116.66568 1.1888448 1.1303764 1.2473132
221 Eastern Broadleaf Forest east 7170 3490 0.2118160 -0.0373764 0.4610084 0.0000000 -0.0090147 0.0090147 0.8317337 0.7810259 0.8824414 30.540702 25.9727555 35.10865 162.50411 147.899022 177.10920 134.68414 117.01892 152.34937 1.3329128 1.2047471 1.4610786
222 Midwest Broadleaf Forest east 4877 2401 -0.0460834 -0.4471784 0.3550117 0.0224450 0.0038175 0.0410725 0.8886905 0.8118750 0.9655059 26.487141 22.7313038 30.24298 120.16868 108.484868 131.85248 107.01369 97.01944 117.00793 1.0536407 0.9534643 1.1538171
223 Central Interior Broadleaf Forest east 8783 3725 0.0724004 -0.1438177 0.2886185 0.0000000 -0.0102390 0.0102390 0.7809249 0.7286645 0.8331854 31.207745 26.7462045 35.66929 107.40334 99.676437 115.13025 107.77584 98.12105 117.43062 1.2644153 1.1471617 1.3816690
231 Southeastern Mixed Forest east 12347 5691 1.7584838 1.4630660 2.0539017 0.0000000 -0.0085177 0.0085177 0.7243199 0.6965018 0.7521381 24.733949 23.2034139 26.26448 106.78132 99.195302 114.36733 107.97366 95.98608 119.96123 1.4752723 1.3795973 1.5709472
232 Outer Coastal Plain Mixed Forest east 12470 6101 1.0680057 0.7755160 1.3604953 0.0144070 0.0035228 0.0252912 0.7467943 0.7168913 0.7766972 28.350008 26.2601723 30.43984 117.77229 107.263792 128.28078 122.20351 103.55149 140.85553 1.5162934 1.3917433 1.6408436
234 Lower Mississippi Riverine Forest east 1265 714 0.0382065 -0.6806976 0.7571107 NA NA NA NA NA NA 12.524348 -24.9680876 50.01678 832.84146 -4680.032010 6345.71492 5000.00000 -72429.65447 82429.65447 3.1877269 -2.7399232 9.1153769
242 Pacific Lowland Mixed Forest pacific 81 81 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1797 809 0.1992410 -0.4319029 0.8303849 0.0000000 -0.0245663 0.0245663 0.7488833 0.6154953 0.8822713 25.687780 15.9230754 35.45248 100.74277 83.248507 118.23703 104.42177 88.11996 120.72357 1.1478928 0.9324216 1.3633639
255 Prairie Parkland (Subtropical) pacific 663 293 -0.1598090 -0.9069202 0.5873022 0.0000000 -0.0522822 0.0522822 0.7729398 0.6090928 0.9367868 20.694043 11.2134875 30.17460 79.86186 61.658187 98.06554 63.52929 49.51970 77.53889 1.1481892 0.8421804 1.4541980
261 California Coastal Chaparral Forest and Shrub pacific 24 24 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 155 155 1.2239516 -3.2300182 5.6779213 NA NA NA NA NA NA 0.000000 -136.5600679 136.56007 1000.00000 -804.464574 2804.46457 1898.22617 -7442.33100 11238.78334 2.7771137 -0.2216429 5.7758703
313 Colorado Plateau Semi-Desert interior west 215 215 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 304 240 0.4888930 -2.4290839 3.4068698 NA NA NA NA NA NA 0.000000 -37.9618826 37.96188 52.42899 -1.716234 106.57421 119.83421 -11.61767 251.28608 2.1713420 -0.2377897 4.5804737
332 Great Plains Steppe interior west 195 106 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 62 62 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 121 120 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 93 61 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6729 2989 0.4244549 0.1245744 0.7243355 0.0254110 0.0144641 0.0363579 0.8214671 0.7777125 0.8652217 17.506687 11.8403129 23.17306 153.07530 132.887777 173.26283 196.14427 150.53438 241.75416 1.6306139 1.4192376 1.8419902
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8034 3700 0.9517694 0.7061059 1.1974328 0.0000000 -0.0082433 0.0082433 0.8478212 0.7855128 0.9101296 38.871490 34.7143586 43.02862 112.93446 105.998009 119.87091 99.91458 94.53922 105.28995 1.1678540 1.0825568 1.2531512
M223 Ozark Broadleaf Forest Meadow east 883 343 -0.6053958 -1.0522432 -0.1585484 0.0766208 0.0412940 0.1119475 0.8905107 0.7506879 1.0303336 0.000000 -93.3960670 93.39607 343.99698 -1002.514773 1690.50873 1654.41165 -19140.77724 22449.60055 3.2937215 -4.0057665 10.5932095
M231 Ouachita Mixed Forest east 988 481 0.5134884 -0.5368625 1.5638393 0.0077329 -0.0362649 0.0517307 0.7642262 0.6122847 0.9161677 16.669136 0.7341976 32.60408 175.75451 -51.246800 402.75582 420.56722 -766.18859 1607.32303 2.1467388 0.4631696 3.8303080
M242 Cascade Mixed Forest pacific 3179 3176 -0.1806076 -1.1444145 0.7831992 0.0000000 -0.0295146 0.0295146 1.1019213 0.9671674 1.2366752 3.554237 -23.8579198 30.96639 568.48059 386.391317 750.56986 667.30946 326.11626 1008.50266 2.2162649 1.7690691 2.6634607
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1963 1963 0.0592276 -1.1060519 1.2245071 0.1887636 0.1653016 0.2122257 0.7151681 0.5373863 0.8929498 0.000000 -49.7841398 49.78414 505.48187 249.528689 761.43505 905.74901 -314.98988 2126.48791 2.7254405 1.6285474 3.8223335
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 19 19 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 362 362 -1.8157315 -2.4780584 -1.1534046 0.0423700 -0.0070057 0.0917456 0.5049877 0.2394459 0.7705295 54.768802 23.9733782 85.56423 184.32447 105.576614 263.07233 158.85154 109.66869 208.03438 0.8168324 0.5032028 1.1304621
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1711 1711 -1.0705976 -1.6464275 -0.4947678 0.0178205 -0.0049652 0.0406063 0.6431528 0.5616230 0.7246825 41.571559 30.7551625 52.38796 135.46943 103.514440 167.42443 212.14212 166.96002 257.32422 1.2343633 1.0135251 1.4552014
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2649 2648 0.7331242 -0.7556754 2.2219239 0.0380474 0.0116674 0.0644274 0.6319656 0.5408357 0.7230954 25.717902 16.6111486 34.82465 99.70475 65.076091 134.33342 210.36985 174.87141 245.86829 1.2406376 1.0563039 1.4249713
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1675 1675 2.4994612 -1.3518126 6.3507349 0.0148648 -0.0191073 0.0488368 0.7076774 0.5990745 0.8162802 17.720879 6.6219799 28.81978 88.45316 33.639406 143.26692 132.83193 121.86747 143.79639 0.9793045 0.8817043 1.0769048
M334 Black Hills Coniferous Forest interior west 362 170 -1.0302125 -1.9899535 -0.0704714 0.0054010 -0.0562644 0.0670664 0.7993264 0.6133402 0.9853125 0.000000 -151.3293796 151.32938 137.94375 -293.146235 569.03374 772.76960 -7135.30221 8680.84140 3.1376453 -6.5672504 12.8425411
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 213 213 -1.8859784 -2.6271118 -1.1448450 0.0000000 -0.1143395 0.1143395 0.5042656 0.2591273 0.7494039 36.458606 17.9001475 55.01706 126.50101 75.154935 177.84709 150.15616 116.77947 183.53286 0.9314925 0.5980113 1.2649737

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map #2

plot phi (effect of DeltaPDSI)

plot alpha (biomass compensation effect)

plot a coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 12 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 12 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US  0.55968415
## 2       pacific -0.05524554
## 3          east  0.66740389
## 4 interior west  0.42071032

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.014754084
## 2       pacific  0.065098909
## 3          east  0.006528787
## 4 interior west  0.022812632

alpha (biomass compensation effect)

##          region weighted.alpha
## 1     entire US      0.7600027
## 2       pacific      0.9012734
## 3          east      0.7731147
## 4 interior west      0.5803015

Calculations - weighted averages subsetted to 15 ecoprovinces

  • 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332

ge

##          region weighted.ge
## 1     entire US  0.62621417
## 2       pacific -0.08899515
## 3          east  0.71149013
## 4 interior west  0.73312423

phi

##          region weighted.phi
## 1     entire US  0.014572771
## 2       pacific  0.072104104
## 3          east  0.005578167
## 4 interior west  0.038047400

alpha

##          region weighted.alpha
## 1     entire US      0.7799773
## 2       pacific      0.9541889
## 3          east      0.7673245
## 4 interior west      0.6319656